PROBABILITY & STATS FOR ENGINEERING &SCI
9th Edition
ISBN: 9781285099804
Author: DEVORE
Publisher: CENGAGE L
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Chapter 13.2, Problem 15E
No tortilla chip aficionado likes soggy chips, so it is important to find characteristics of the production process that produce chips with an appealing texture. The following data on x = frying time (sec) and y = moisture content (%) appeared in the article “Thermal and Physical Properties of Tortilla Chips as a
| x | 5 | 10 | 15 | 20 | 25 | 30 | 45 | 60 |
| y | 16.3 | 9.7 | 8.1 | 4.2 | 3.4 | 2.9 | 1.9 | 1.3 |
a. Construct a
b. Construct a scatterplot of the (ln(x), ln(y)) pairs and comment.
c. What probabilistic relationship between x and y is suggested by the linear pattern in the plot of part (b)?
d. Predict the value of moisture content when frying time is 20, in a way that conveys information about reliability and precision.
e. Analyze the residuals from fitting the simple linear regression model to the transformed data and comment.
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Wrinkle recovery angle and tensile strength are the two most important characteristics for evaluating the performance of crosslinked cotton fabric. An increase in the degree of crosslinking, as determined by ester carboxyl band absorbance, improves the wrinkle
resistance of the fabric (at the expense of reducing mechanical strength). The accompanying data on x = absorbance and y = wrinkle resistance angle was read from a graph in the paper "Predicting the Performance of Durable Press Finished Cotton Fabric with
Infrared Spectroscopy".†
x 0.115 0.126 0.183 0.246 0.282 0.344 0.355 0.452 0.491 0.554 0.651
y 334 342 355 363
365 372 381 392
400 412 420
Here is regression output from Minitab:
Predictor
Constant
absorb
S = 3.60498
Coef
321.878
156.711
SOURCE
Regression
Residual Error
Total
SE Coef
2.483
6.464
R-Sq = 98.5%
DF
1
9
10
SS
7639.0
117.0
7756.0
T
129.64
24.24
0.000
0.000
R-Sq (adj) = 98.3%
MS
7639.0
13.0
F
P
587.81
(a) Does the simple linear regression model appear to be…
Wrinkle recovery angle and tensile strength are the two most important characteristics for evaluating the performance of crosslinked cotton fabric. An increase in the degree of crosslinking, as determined by ester carboxyl band absorbance, improves the wrinkle resistance of the fabric (at the expense of reducing mechanical
strength). The accompanying data on x = absorbance and y = wrinkle resistance angle was read from a graph in the paper "Predicting the Performance of Durable Press Finished Cotton Fabric with Infrared Spectroscopy".t
半
0.115 0.126 0.183 0.246 0.282 0.344 0.355 0.452 0.491 0.554 0.651
334 342
355
363
365
372
381
392
400
412
420
Here is regression output from Minitab:
Predictor
Coef
SE Coef
P
Constant
321.878
2.483
129.64
0.000
absorb
156.711
6.464
24.24
0.000
S = 3.60498
R-Sq = 98.5%
R-Są (adj) - 98.3%
SOURCE
DF
MS
F
P
Regression
1
7639.0
7639.0
587.81
0.000
Residual Error
9
117.0
13.0
Total
10
7756.0
(a) Does the simple linear regression model appear to be…
Wrinkle recovery angle and tensile strength are the two most important characteristics for evaluating the performance of crosslinked cotton fabric. An increase in the degree of crosslinking, as
determined by ester carboxyl band absorbance, improves the wrinkle resistance of the fabric (at the expense of reducing mechanical strength). The accompanying data on x = absorbance and
y = wrinkle resistance angle was read from a graph in the paper "Predicting the Performance of Durable Press Finished Cotton Fabric with Infrared Spectroscopy".t
x 0.115 0.126 0.183 0.246 0.282 0.344 0.355 0.452 0.491 0.554 0.651
y
334 342 355
363
365 372 381
400
392
412 420
Here is regression output from Minitab:
Predictor
Constant
absorb
S = 3.60498
Coef
321.878
156.711
SOURCE
Regression
Residual Error
Total
R-Sq= 98.5%
DF
SE Coef
2.483
6.464
1
9
10
SS
7639.0
117.0
7756..0
T
129.64
24.24
P
0.000
0.000.
R-Sq (adj) 98.3%
MS
7639.0
13.0
F
587.81
(a) Does the simple linear regression model appear to be appropriate?…
Chapter 13 Solutions
PROBABILITY & STATS FOR ENGINEERING &SCI
Ch. 13.1 - Suppose the variables x = commuting distance and y...Ch. 13.1 - Prob. 2ECh. 13.1 - Prob. 3ECh. 13.1 - Prob. 4ECh. 13.1 - As the air temperature drops, river water becomes...Ch. 13.1 - The accompanying scatterplot is based on data...Ch. 13.1 - Prob. 7ECh. 13.1 - Prob. 8ECh. 13.1 - Consider the following four (x, y) data sets; the...Ch. 13.1 - a. Show that i=1nei=0 when the eis are the...
Ch. 13.1 - Prob. 11ECh. 13.1 - Prob. 12ECh. 13.1 - Prob. 13ECh. 13.1 - If there is at least one x value at which more...Ch. 13.2 - No tortilla chip aficionado likes soggy chips, so...Ch. 13.2 - Polyester fiber ropes are increasingly being used...Ch. 13.2 - The following data on mass rate of burning x and...Ch. 13.2 - Failures in aircraft gas turbine engines due to...Ch. 13.2 - Prob. 19ECh. 13.2 - Prob. 20ECh. 13.2 - Mineral mining is one of the most important...Ch. 13.2 - Prob. 22ECh. 13.2 - Prob. 23ECh. 13.2 - Kyphosis refers to severe forward flexion of the...Ch. 13.2 - Prob. 25ECh. 13.3 - The following data on y 5 glucose concentration...Ch. 13.3 - The viscosity (y) of an oil was measured by a cone...Ch. 13.3 - Prob. 29ECh. 13.3 - The accompanying data was extracted from the...Ch. 13.3 - The accompanying data on y 5 energy output (W) and...Ch. 13.3 - Prob. 32ECh. 13.3 - Prob. 33ECh. 13.3 - The following data resulted from an experiment to...Ch. 13.3 - The article The Respiration in Air and in Water of...Ch. 13.4 - Cardiorespiratory fitness is widely recognized as...Ch. 13.4 - A trucking company considered a multiple...Ch. 13.4 - Let y = wear life of a bearing, x1 = oil...Ch. 13.4 - Let y = sales at a fast-food outlet (1000s of ),...Ch. 13.4 - The article cited in Exercise 49 of Chapter 7 gave...Ch. 13.4 - The article A Study of Factors Affecting the Human...Ch. 13.4 - An investigation of a die-casting process resulted...Ch. 13.4 - Prob. 43ECh. 13.4 - The accompanying Minitab regression output is...Ch. 13.4 - The article Analysis of the Modeling Methodologies...Ch. 13.4 - A regression analysis carried out to relate y =...Ch. 13.4 - Efficient design of certain types of municipal...Ch. 13.4 - An experiment to investigate the effects of a new...Ch. 13.4 - Prob. 49ECh. 13.4 - Prob. 50ECh. 13.4 - The article Optimization of Surface Roughness in...Ch. 13.4 - Utilization of sucrose as a carbon source for the...Ch. 13.4 - Prob. 53ECh. 13.4 - Prob. 54ECh. 13.5 - The article The Influence of Honing Process...Ch. 13.5 - Prob. 56ECh. 13.5 - In the accompanying table, we give the smallest...Ch. 13.5 - Prob. 58ECh. 13.5 - Prob. 59ECh. 13.5 - Pillar stability is a most important factor to...Ch. 13.5 - Prob. 61ECh. 13.5 - Prob. 62ECh. 13.5 - Prob. 63ECh. 13.5 - Prob. 64ECh. 13 - Curing concrete is known to be vulnerable to shock...Ch. 13 - Prob. 66SECh. 13 - The article Validation of the Rockport Fitness...Ch. 13 - Feature recognition from surface models of...Ch. 13 - Air pressure (psi) and temperature (F) were...Ch. 13 - An aeronautical engineering student carried out an...Ch. 13 - An ammonia bath is the one most widely used for...Ch. 13 - The article An Experimental Study of Resistance...Ch. 13 - The accompanying data on x = frequency (MHz) and y...Ch. 13 - Prob. 74SECh. 13 - Prob. 75SECh. 13 - The article Chemithermomechanical Pulp from Mixed...Ch. 13 - Prob. 77SECh. 13 - Prob. 78SECh. 13 - Prob. 79SECh. 13 - Prob. 80SECh. 13 - Prob. 81SECh. 13 - Prob. 82SECh. 13 - Prob. 83SE
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